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Added examples from MILP-paper. 

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dehnert 12 years ago
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  1. 130
      examples/mdp/csma/csma2_2.nm
  2. 128
      examples/mdp/csma/csma2_4.nm
  3. 170
      examples/mdp/firewire/impl/firewire.nm
  4. 218
      examples/mdp/wlan/wlan0_collide.nm
  5. 225
      examples/mdp/wlan/wlan2_collide.nm

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examples/mdp/csma/csma2_2.nm
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// CSMA/CD protocol - probabilistic version of kronos model (3 stations)
// gxn/dxp 04/12/01
mdp
// note made changes since cannot have strict inequalities
// in digital clocks approach and suppose a station only sends one message
// simplified parameters scaled
const int sigma=1; // time for messages to propagate along the bus
const int lambda=30; // time to send a message
// actual parameters
const int N = 2; // number of processes
const int K = 2; // exponential backoff limit
const int slot = 2*sigma; // length of slot
// const int M = floor(pow(2, K))-1 ; // max number of slots to wait
const int M = 3 ; // max number of slots to wait
//const int lambda=782;
//const int sigma=26;
// formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1);
// formula min_collisions = min(cd1,cd2);
// formula max_collisions = max(cd1,cd2);
//----------------------------------------------------------------------------------------------------------------------------
// the bus
module bus
b : [0..2];
// b=0 - idle
// b=1 - active
// b=2 - collision
// clocks of bus
y1 : [0..sigma+1]; // time since first send (used find time until channel sensed busy)
y2 : [0..sigma+1]; // time since second send (used to find time until collision detected)
// a sender sends (ok - no other message being sent)
[send1] (b=0) -> (b'=1);
[send2] (b=0) -> (b'=1);
// a sender sends (bus busy - collision)
[send1] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send2] (b=1|b=2) & (y1<sigma) -> (b'=2);
// finish sending
[end1] (b=1) -> (b'=0) & (y1'=0);
[end2] (b=1) -> (b'=0) & (y1'=0);
// bus busy
[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b);
// collision detected
[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
// time passage
[time] (b=0) -> (y1'=0); // value of y1/y2 does not matter in state 0
[time] (b=1) -> (y1'=min(y1+1,sigma+1)); // no invariant in state 1
[time] (b=2) & (y2<sigma) -> (y1'=min(y1+1,sigma+1)) & (y2'=min(y2+1,sigma+1)); // invariant in state 2 (time until collision detected)
endmodule
//----------------------------------------------------------------------------------------------------------------------------
// model of first sender
module station1
// LOCAL STATE
s1 : [0..5];
// s1=0 - initial state
// s1=1 - transmit
// s1=2 - collision (set backoff)
// s1=3 - wait (bus busy)
// s1=4 - successfully sent
// LOCAL CLOCK
x1 : [0..max(lambda,slot)];
// BACKOFF COUNTER (number of slots to wait)
bc1 : [0..M];
// COLLISION COUNTER
cd1 : [0..K];
// start sending
[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending
[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff
// transmitting
[time] (s1=1) & (x1<lambda) -> (x1'=min(x1+1,lambda)); // let time pass
[end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished
[cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected (increment backoff counter)
[cd] !(s1=1) -> (s1'=s1); // add loop for collision detection when not important
// set backoff (no time can pass in this state)
// probability depends on which transmission this is (cd1)
[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ;
[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ;
// wait until backoff counter reaches 0 then send again
[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
[time] (s1=3) & (x1=slot) & (bc1>0) -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots)
[send1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=1) & (x1'=0); // finished backoff (bus appears free)
[busy1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // finished backoff (bus busy)
// once finished nothing matters
[time] (s1>=4) -> (x1'=0);
endmodule
//----------------------------------------------------------------------------------------------------------------------------
// construct further stations through renaming
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule
//----------------------------------------------------------------------------------------------------------------------------
// reward structure for expected time
rewards "time"
[time] true : 1;
endrewards
//----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);

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// CSMA/CD protocol - probabilistic version of kronos model (3 stations)
// gxn/dxp 04/12/01
mdp
// note made changes since cannot have strict inequalities
// in digital clocks approach and suppose a station only sends one message
// simplified parameters scaled
const int sigma=1; // time for messages to propagate along the bus
const int lambda=30; // time to send a message
// actual parameters
const int N = 2; // number of processes
const int K = 4; // exponential backoff limit
const int slot = 2*sigma; // length of slot
const int M = 15 ; // max number of slots to wait
//const int lambda=782;
//const int sigma=26;
//----------------------------------------------------------------------------------------------------------------------------
// the bus
module bus
b : [0..2];
// b=0 - idle
// b=1 - active
// b=2 - collision
// clocks of bus
y1 : [0..sigma+1]; // time since first send (used find time until channel sensed busy)
y2 : [0..sigma+1]; // time since second send (used to find time until collision detected)
// a sender sends (ok - no other message being sent)
[send1] (b=0) -> (b'=1);
[send2] (b=0) -> (b'=1);
// a sender sends (bus busy - collision)
[send1] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send2] (b=1|b=2) & (y1<sigma) -> (b'=2);
// finish sending
[end1] (b=1) -> (b'=0) & (y1'=0);
[end2] (b=1) -> (b'=0) & (y1'=0);
// bus busy
[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b);
// collision detected
[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
// time passage
[time] (b=0) -> (y1'=0); // value of y1/y2 does not matter in state 0
[time] (b=1) -> (y1'=min(y1+1,sigma+1)); // no invariant in state 1
[time] (b=2) & (y2<sigma) -> (y1'=min(y1+1,sigma+1)) & (y2'=min(y2+1,sigma+1)); // invariant in state 2 (time until collision detected)
endmodule
//----------------------------------------------------------------------------------------------------------------------------
// model of first sender
module station1
// LOCAL STATE
s1 : [0..5];
// s1=0 - initial state
// s1=1 - transmit
// s1=2 - collision (set backoff)
// s1=3 - wait (bus busy)
// s1=4 - successfully sent
// LOCAL CLOCK
x1 : [0..max(lambda,slot)];
// BACKOFF COUNTER (number of slots to wait)
bc1 : [0..M];
// COLLISION COUNTER
cd1 : [0..K];
// start sending
[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending
[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff
// transmitting
[time] (s1=1) & (x1<lambda) -> (x1'=min(x1+1,lambda)); // let time pass
[end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished
[cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected (increment backoff counter)
[cd] !(s1=1) -> (s1'=s1); // add loop for collision detection when not important
// set backoff (no time can pass in this state)
// probability depends on which transmission this is (cd1)
[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ;
[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ;
[] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (bc1'=0) + 1/8 : (s1'=3) & (bc1'=1) + 1/8 : (s1'=3) & (bc1'=2) + 1/8 : (s1'=3) & (bc1'=3) + 1/8 : (s1'=3) & (bc1'=4) + 1/8 : (s1'=3) & (bc1'=5) + 1/8 : (s1'=3) & (bc1'=6) + 1/8 : (s1'=3) & (bc1'=7) ;
[] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (bc1'=0) + 1/16 : (s1'=3) & (bc1'=1) + 1/16 : (s1'=3) & (bc1'=2) + 1/16 : (s1'=3) & (bc1'=3) + 1/16 : (s1'=3) & (bc1'=4) + 1/16 : (s1'=3) & (bc1'=5) + 1/16 : (s1'=3) & (bc1'=6) + 1/16 : (s1'=3) & (bc1'=7) + 1/16 : (s1'=3) & (bc1'=8) + 1/16 : (s1'=3) & (bc1'=9) + 1/16 : (s1'=3) & (bc1'=10) + 1/16 : (s1'=3) & (bc1'=11) + 1/16 : (s1'=3) & (bc1'=12) + 1/16 : (s1'=3) & (bc1'=13) + 1/16 : (s1'=3) & (bc1'=14) + 1/16 : (s1'=3) & (bc1'=15) ;
// wait until backoff counter reaches 0 then send again
[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
[time] (s1=3) & (x1=slot) & (bc1>0) -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots)
[send1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=1) & (x1'=0); // finished backoff (bus appears free)
[busy1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // finished backoff (bus busy)
// once finished nothing matters
[time] (s1>=4) -> (x1'=0);
endmodule
//----------------------------------------------------------------------------------------------------------------------------
// construct further stations through renaming
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule
//----------------------------------------------------------------------------------------------------------------------------
// reward structure for expected time
rewards "time"
[time] true : 1;
endrewards
//----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);

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// firewire protocol with integer semantics
// dxp/gxn 14/06/01
// CLOCKS
// x1 (x2) clock for node1 (node2)
// y1 and y2 (z1 and z2) clocks for wire12 (wire21)
mdp
// maximum and minimum delays
// fast
const int rc_fast_max = 85;
const int rc_fast_min = 76;
// slow
const int rc_slow_max = 167;
const int rc_slow_min = 159;
// delay caused by the wire length
const int delay;
// probability of choosing fast
const double fast;
const double slow=1-fast;
module wire12
// local state
w12 : [0..9];
// 0 - empty
// 1 - rec_req
// 2 - rec_req_ack
// 3 - rec_ack
// 4 - rec_ack_idle
// 5 - rec_idle
// 6 - rec_idle_req
// 7 - rec_ack_req
// 8 - rec_req_idle
// 9 - rec_idle_ack
// clock for wire12
y1 : [0..delay+1];
y2 : [0..delay+1];
// empty
// do not need y1 and y2 to increase as always reset when this state is left
// similarly can reset y1 and y2 when we re-enter this state
[snd_req12] w12=0 -> (w12'=1) & (y1'=0) & (y2'=0);
[snd_ack12] w12=0 -> (w12'=3) & (y1'=0) & (y2'=0);
[snd_idle12] w12=0 -> (w12'=5) & (y1'=0) & (y2'=0);
[time] w12=0 -> (w12'=w12);
// rec_req
[snd_req12] w12=1 -> (w12'=1);
[rec_req12] w12=1 -> (w12'=0) & (y1'=0) & (y2'=0);
[snd_ack12] w12=1 -> (w12'=2) & (y2'=0);
[snd_idle12] w12=1 -> (w12'=8) & (y2'=0);
[time] w12=1 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_req_ack
[snd_ack12] w12=2 -> (w12'=2);
[rec_req12] w12=2 -> (w12'=3);
[time] w12=2 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_ack
[snd_ack12] w12=3 -> (w12'=3);
[rec_ack12] w12=3 -> (w12'=0) & (y1'=0) & (y2'=0);
[snd_idle12] w12=3 -> (w12'=4) & (y2'=0);
[snd_req12] w12=3 -> (w12'=7) & (y2'=0);
[time] w12=3 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_ack_idle
[snd_idle12] w12=4 -> (w12'=4);
[rec_ack12] w12=4 -> (w12'=5);
[time] w12=4 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_idle
[snd_idle12] w12=5 -> (w12'=5);
[rec_idle12] w12=5 -> (w12'=0) & (y1'=0) & (y2'=0);
[snd_req12] w12=5 -> (w12'=6) & (y2'=0);
[snd_ack12] w12=5 -> (w12'=9) & (y2'=0);
[time] w12=5 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_idle_req
[snd_req12] w12=6 -> (w12'=6);
[rec_idle12] w12=6 -> (w12'=1);
[time] w12=6 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_ack_req
[snd_req12] w12=7 -> (w12'=7);
[rec_ack12] w12=7 -> (w12'=1);
[time] w12=7 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_req_idle
[snd_idle12] w12=8 -> (w12'=8);
[rec_req12] w12=8 -> (w12'=5);
[time] w12=8 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
// rec_idle_ack
[snd_ack12] w12=9 -> (w12'=9);
[rec_idle12] w12=9 -> (w12'=3);
[time] w12=9 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1));
endmodule
module node1
// clock for node1
x1 : [0..168];
// local state
s1 : [0..8];
// 0 - root contention
// 1 - rec_idle
// 2 - rec_req_fast
// 3 - rec_req_slow
// 4 - rec_idle_fast
// 5 - rec_idle_slow
// 6 - snd_req
// 7- almost_root
// 8 - almost_child
// added resets to x1 when not considered again until after rest
// removed root and child (using almost root and almost child)
// root contention immediate state)
[snd_idle12] s1=0 -> fast : (s1'=2) & (x1'=0) + slow : (s1'=3) & (x1'=0);
[rec_idle21] s1=0 -> (s1'=1);
// rec_idle immediate state)
[snd_idle12] s1=1 -> fast : (s1'=4) & (x1'=0) + slow : (s1'=5) & (x1'=0);
[rec_req21] s1=1 -> (s1'=0);
// rec_req_fast
[rec_idle21] s1=2 -> (s1'=4);
[snd_ack12] s1=2 & x1>=rc_fast_min -> (s1'=7) & (x1'=0);
[time] s1=2 & x1<rc_fast_max -> (x1'=min(x1+1,168));
// rec_req_slow
[rec_idle21] s1=3 -> (s1'=5);
[snd_ack12] s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0);
[time] s1=3 & x1<rc_slow_max -> (x1'=min(x1+1,168));
// rec_idle_fast
[rec_req21] s1=4 -> (s1'=2);
[snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0);
[time] s1=4 & x1<rc_fast_max -> (x1'=min(x1+1,168));
// rec_idle_slow
[rec_req21] s1=5 -> (s1'=3);
[snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0);
[time] s1=5 & x1<rc_slow_max -> (x1'=min(x1+1,168));
// snd_req
// do not use x1 until reset (in state 0 or in state 1) so do not need to increase x1
// also can set x1 to 0 upon entering this state
[rec_req21] s1=6 -> (s1'=0);
[rec_ack21] s1=6 -> (s1'=8);
[time] s1=6 -> (s1'=s1);
// almost root (immediate)
// loop in final states to remove deadlock
[] s1=7 & s2=8 -> (s1'=s1);
[] s1=8 & s2=7 -> (s1'=s1);
[time] s1=7 -> (s1'=s1);
[time] s1=8 -> (s1'=s1);
endmodule
// construct remaining automata through renaming
module wire21=wire12[w12=w21, y1=z1, y2=z2,
snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21,
rec_req12=rec_req21, rec_idle12=rec_idle21, rec_ack12=rec_ack21]
endmodule
module node2=node1[s1=s2, s2=s1, x1=x2,
rec_req21=rec_req12, rec_idle21=rec_idle12, rec_ack21=rec_ack12,
snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21]
endmodule
// reward structures
// time
rewards "time"
[time] true : 1;
endrewards
// time nodes sending
rewards "time_sending"
[time] (w12>0 | w21>0) : 1;
endrewards
label "elected" = ((s1=8) & (s2=7)) | ((s1=7) & (s2=8));

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// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =16
// this means that MAX_BACKOFF IS 2
const int MAX_BACKOFF = 0;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
// formula busy = c1>0 | c2>0;
// channel is free
// formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..1];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..1];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & (c1>0 | c2>0) -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & (c1=0 & c2=0) -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & (c1>0 | c2>0) -> (s1'=6);
// find that channel is free
[] s1=6 & (c1=0 & c2=0) -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & (c1=0 & c2=0))) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "oneCollision" = col=1;
label "twoCollisions" = col=2;

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examples/mdp/wlan/wlan2_collide.nm
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// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =63
// this means that MAX_BACKOFF IS 2
const int MAX_BACKOFF = 2;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is (c1>0 | c2>0)
// formula busy = c1>0 | c2>0;
// channel is (c1=0 & c2=0)
// formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until (c1=0 & c2=0) before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until (c1=0 & c2=0) in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..3];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel (c1>0 | c2>0) so wait until (c1=0 & c2=0)
[] s1=1 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
// WAIT UNTIL (c1=0 & c2=0) BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & (c1>0 | c2>0) -> (s1'=2);
// find that channel is (c1=0 & c2=0) so check its (c1=0 & c2=0) for DIFS before setting backoff
[] s1=2 & (c1=0 & c2=0) -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// found channel (c1>0 | c2>0) so wait until (c1=0 & c2=0)
[] s1=3 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 2
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel (c1>0 | c2>0)
[] s1=5 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// WAIT UNTIL (c1=0 & c2=0) IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & (c1>0 | c2>0) -> (s1'=6);
// find that channel is (c1=0 & c2=0)
[] s1=6 & (c1=0 & c2=0) -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel (c1>0 | c2>0)
[] s1=7 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and (c1>0 | c2>0): go into backoff
[] s1=10 & c1=0 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and (c1=0 & c2=0): let time pass
[time] s1=10 & c1=0 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is (c1=0 & c2=0))
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & (c1=0 & c2=0))) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and (c1>0 | c2>0): go into backoff
[] s1=11 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and (c1=0 & c2=0): let time pass
[time] s1=11 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "oneCollision" = col=1;
label "twoCollisions" = col=2;
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